The Beauty of Mathematics in Marketing Mix Modeling

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The most controversial subject during school which caused hatred or passion is Mathematics. But Math is about truth regardless of your opinion; it is true that when you group 5 of something with another 5 of that something you will get 10 of that something, everyone agrees that this is true and there is no reason to inject any unreasonable argument to this fact. The only thing that you can argue about in math is that whether it is a feature of existence independent of us or if it is a feature of our human mind. In both cases math is very powerful and effective language to explain things around us.

In marketing mix modeling, we use mathematics to explain sales of products in numbers and relationships with explanatory variables which we sometimes call support variables or marketing levers like advertising, promotions, social activities, distribution, price, macro-economy etc., by looking into patterns and regularities in history and devising predictive mathematical models based on set of equations. We use mathematics to simplify the way we look at how and why sales behave the way it behaves in a complicated and competitive environment. But this should be the result of a long and thorough process. It is like a pyramid, where we gather lot of data first, and then reduce the long list of variables into a small list of variables that marketers can control or monitor.

But using only mathematics without having the business acumen could be risky. Especially that mathematics today is embedded in data analytics tools that are accessible by everyone. A mathematician with a good business knowledge knows how to treat variables before plugging them in equations like transforming advertising variables into ad-stocks and decay variables, also knows if the outcome equations are only over-fitting the data i.e. only explaining the current data without having the characteristics of predicting future results based on new data.

Another pitfall is missing variables that are not apparent at the beginning but could play a crucial role in the marketing mix. A brand might have a weighted distribution equals to 98% and yet have variants or SKUs not reaching 60% of the weighted distribution. In this case, including only the weighted distribution in the equation is not fair because the model will show that you can no longer increase your sales on the basis of increase in distribution, and yet there is still room by distributing more formats.

As sales could not possibly be the result of only one variable, analysts should be able to be flexible to  use different techniques and analyze many variables as possible to explain sales and at the same time be relevant to the business problem while maintaining scientific and mathematical approach.

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